A shielding device of the generic type is already known from the connection strip disclosed in U.S. Pat. No. 5,160,273. Here, the problem of crosstalk between adjacent insulation-piercing terminal contact elements of the connection strip is solved by the insertion of a multiplicity of electrically conductive shielding plates between the individual pairs of insulation-piercing terminal contact elements. The problem of crosstalk occurs when transmitting large volumes of information via electrical lines, the information being transmitted at high frequencies. Transmitting at high frequencies produces radiation and interference between adjacent lines, particularly when these lines are arranged close besides one another in the connection strip. Electrically conductive shielding plates are inserted between a pair of insulation-piercing terminal contact elements, the spacing between two adjacent pairs of insulation-piercing terminal contact elements being larger than the spacing between adjacent insulation-piercing terminal contact elements in a pair. The shielding plates are in this case inserted between pairs of insulation-piercing terminal contact elements in slots which extend transversely to the longitudinal direction of the plastic body of the connection strip, and contact the base rail situated in the longitudinal direction inside the plastic body. A disadvantage of this is that, when fitting the component into the plastic body, it is first necessary to fit the base rail, which has contact tongues for contacting the individual shielding plates, and that is subsequently necessary to push the individual shielding plates into the connection strip. Consequently, the complexity of assembly is relatively high in order to provide the connection strip with the shielding device for high transmission rates in telecommunications and data engineering.